Antifoggants for photographic developers



United States Patent ANT IFOGGAN TS FOR PHOTOGRAPHIC DEVELOPERSCatherine M. Spath, Rochester, N. Y., assignor to Eastman Kodak Company,Rochester, N. Y., a corporation of New Jersey No Drawing. ApplicationAugust 3, 1956 Serial No. 602,067

11 Claims. (Cl. 96-22) This invention relates to photographicdevelopers, and more particularly, a method of inhibiting or preventingfog during development.

' It is known that when a developer acts upon an exposed emulsion layer,some of the silver halide grains which have not been exposed to light orradiation are reduced to metallic silver. This metallic silver in theunexposed portions of the emulsion results in unwanted density and thisdensity is known as fog. Fog may be formed as a result of the chemicalcharacteristics of the developing agent, the particular silver halideemulsion, or both. In order to produce efiective results in variousphotographic processes, it is, accordingly, necessary to inhibit fogboth in the emulsion layers and in the photographic developingsolutions. While it may be important to inhibit fog as much as possiblein black-and-white photography, it is even more important in reversalcolor processes, where the exposed emulsion layers are given a firstdevelopment in a black-and-white developer, followed by reversalexposure and development in a color developer. Otherwise a proper colorbalance is not obtained since sutficient silver halide is not availablein the appropriate areas of the emulsion layer for subsequentdevelopment with a color developer.

The unwanted density occurring as a result of the action of theblack-and-white developer is particularly apparent in those portions ofthe emulsion layers intended to record the cyan image, i. e., where nored area, or a reduced amount of red, is present in the originalsubject. A similar effect occurs in the emulsion layers intended torecord the magenta and yellow images.

I have now found an improved means of controlling the unwanted densityresulting during black-and-white development of photographic silverhalide emulsions. Silver halide emulsions which have been subjected to afirst development for producing a black-and-white image, followed atsome later stage by color development for producing a cyan image,and'which contain a fog-inhibiting agent in the first developer asoutlined below, have improved contrast and color density.

It is, accordingly, an object of my invention to provide improveddevelopers in photographic processes. Another object is to provide amethod of inhibiting the fog resulting from the action of certainblack-and-white developers. Still another object is to improve theaccuracy of rendition of color images, particularly in the cyan layer ofmultilayer photographic elements which have been differentiallysensitized to record specific regions of the spectrum. Other objectswill become apparent from a consideration of the following descriptionand examples.

According to my invention, I provide improved photographic developerscontaining 4-carboxythiazolidines, or water-soluble salts thereof, inaddition to the usual alkaline agent and black-and-white developingagent.

2,860,976 Patented Nov. 18, 19 58 "ice 2 The 4-carboxythiazolidinesuseful in practicing my invention can advantageously be represented bythe following general formula:

posits of silver in unwanted portions of the. emulsion.

R7o OH; H s wherein R represents a hydrogen atom, an alkyl group (e. g.,methyl, ethyl, etc.), especially a lower alkyl group,

tassium, lithium, etc.), an ammonium ion, or an organic ammonium ion,such as pyridinium (R is hydrogen), tr1- ethyl ammonium (R is hydrogen-,etc. The term car boxyl as used herein is intended to define the COOHgroup as well as water-soluble derivatives thereof. If desired, thecompounds of Formula I can be added to the strongly alkaline developingagents in the form of their esters which are easily hydrolyzed, such asmethyl or ethyl esters, to give the desired water-soluble alkali metalsalts.

The 4-carboxythiazolidines useful in practicing my invention are addedto the developers commonly employed in the photographic art forproducing black-and-white images. Such developers include the compoundsknown as polyhydroxybenzenes (e. g., hydroquinone, catechol, pyrogallol,etc.), and N-substituted aminophenols (e. g., N-methylaminophenols,N-ethylaminophenols, 'etc.) or mixtures of such developers. Prominentamong such developing agents for the rapid development ofphotographicimages are those comprising hydroquinone and Elon (p-N-methylaminophenol). While such developing agentsof the emulsion whereno exposure took place. The additives of my invention eliminate ormaterially reduce delayers.

It has been previously proposed to incorporate various4-carboxythiazolidines in small quantities in photographicsilver halideemulsions, however, these additives cause a loss in sensitivity in theemulsions in certain cases and" sufficient quantity thereof does notfind its-way into the developing solutions to be of any materialbenefit. It has been unexpectedly found that addition of these4-carboxythiazolidines to black-and-white developers has a markedbeneficial effect on the characteristics of therresulting image,particularly in photographic reversal color processes.

4-carboxythiazolidines (and water-soluble salts thereof) which have beenfound particularly useful in practicing my invention include thefollowing;

( 1 4-carboxythiazolidine (2) 4-carboxy-2-(p-nitrophenyl)thiazolidine(3) 4 carboxy 2 (4 hydroxy 3 methoxyphenyl thiazolidine (4)4-carboxy-2-(p-hydroxyphenyl)thiazolidine- 54-carboxy-2-(p-chlorophenyl) thiazolidine (6)4-carboxy-2-(o-chlorophenyl)thiazolidine (7 4-carboxy-2-(m-nitrophenyl)thiazolidine (8) 4-carboxy-2-(o-nitrophenyl)thiazolidine i (9)4-carboxy-2-(p-diethylaminophenyl)thiazolidine (10)4-carboxy-Zm-hexylthiazolidine The above 4-carboxythiazolidines can, beprepared.ac.-

cording to the method described by Tegima et al. in J. Chem. Soc. Japan,Ind. Chem. Sect., vol. 52 (1949), pages 336-8. and vol. 54 (1951), pages648-51.

The 4-carboxythiazolidines employed in the developers of my nvention canbe utilized in various concentrations. depending on the particularemulsions employed and the concentrationof silver halide in theemulsions and concentration of developing agents in the. developers. Ingeneral, not less than 10 mg. per liter of developer of 4-carboxythiazolidine should be employed. The most advantageousconcentration of 4-carboxvthiazolidine compound can be determined bydeveloping a series of test strips of silver halide emulsions whereinthe concentration of the 4-carboxythiazolidine compounds is varied,aswvell as the-concentrationofi-developing a ent (if desired); The usualaddenda can be employed. in thedevelopersa such: as-stronglvalkalineagents (e. g.. sodium carbonate, potassiumcarbonate, sodium hydroxide,ctc.),

restrainers. such'as potassium bromide, stain preventives,

such as alkali metal sulfites. etc.

Myinventionis primarily directed to the development of the ordinarilyemployed gelatino-siliver-halide developmg-out emulsions-e. g.,gelatino-silver-chloride, -chlorobromide. -chloroiodide,-chlorobromiodide. -bromide and -bromiodide. developing-out emulsions.While the results in the following examples were obtained usinggelatinosilver-bromiodide emulsions, excellent results have also beenobtained usingother silver halide emulsions. These emulsions can becoated'in the usual manner on any suitable support, e. g., glass,cellulose nitrate film, cellulose acetate film, polyvinyl acetal resinfilm, paper or metal. Photographic silver halide emulsions useful in myinvention can also contain such addenda as chemical sensitlzers, e. g.,sulfur sensitizers (e. g., allyl thiocarbamide, thiourea, allylisothiocyanate, cystine, etc). various gold compounds (e. g., potassiumchloroaurate, auric trichloride, etc.) (see U. S. Patents 2,540,085;2,597,856 and 2.597315), various azaindene compounds (such as thosedisclosed in U. S. Patent 2,716.062), condensation products of alkyleneoxides, such' as those shown in U. S. Patent 2,400,532, as well as theadditives mentioned in Jones et al. U.. S. application Serial No.575,160, filed March 30, 1956. i

As mentioned above, the advantages of my invention are particularlyoutstanding in reversal color photographic processes This includesprocesses where the color couplersare incorporated in the colordevelopers or where: the color-forming compounds are incorporated in thephotographic emulsions. Where the color-forming compounds' areincorporated in the photographic emulsionsyit. is generally desirable todisperse the-samein-an appropriate dispersing medium, such as is shownin U. S. Patents 2,322,027 or 2,304,940. Typical color-forming compoundswhich can be employed in my invention in clude the following:

COUPLER (1) 1- hydroxy 2[-2',4'-di-tert.amylphenoxy)-nbutylJ-naphthamide (U. S. Patent2,474,293) (2) 1-hydroxy-4phenylazo-4-(p-tert.-butylphenoxy)-2-naphthanilide (U. S. Patent 2,521,908) (3) 2-2,4-di-tert.amylphenoxyacetamino -4,6-dichloro- S-methyl phenol (U. S.Patent 2,725,291) (4) 2-(a-di-tert.amylphenoxy-n-butyrylamino)- 4,6dichloro-t-methyl phenol (5) 6-{a-{4-[a-(2,4-di-tert.amylphenoxy)butyrarnido]phenoxy}acetamido}-2,4-dichloro-3-methyl phenol (6) 2-[3'-(2",4"-diamylphenoxy) -acetamido] -benzamido-4-chloro-5-methylphenol(7) 1-(2,4',6"- trichlorophenyl)-3-[3"-(2',4"'-di-tert.-amylphenoxyacetamido) -benzamidoJ-5-pyrazolone (U. S. Patent 2,600,788)(8) 1-(2',4',6 trichloropl1enyl) 3-[3"-(2",4"'di-tert.-

amylphenoxyacetamido)-benzamido1- 4 -(p methoxyphenylazo)-5-pyrazolone(9) N (4 benzoylacetaminobenzenesulfonyl) N-(vphenylpropyl)-p-toluidine(U. S. Patent 2,298,443)

(10) oc-O-MCthOXYbCIIZOYI-a-ChlOIO-4-[oz-(2,4 di tort.-

amylphenoxy -n-butyramido]-acetanilide (McCrossen U. S. applicationSerial No. 295,806)

(11) a-{3-[a-(2,4-di-tert.amylphenoxy)acetamido]benzoyl}-2-methoxyacetanilide (12) 3-benzoylacetamido-4-methoxy-2,4'-ditert.amylphenoxy acetanilide (13)4-benzoylacetamido-3-methoxy-2',4-di-tert. amylphenoxy acetanilide Theabove couplers are primarily useful for use in photographic silverhalide emulsions as contrasted with;

other couplers which are primarily useful in color. dcvelopers. Couplerswhich are primarily useful in color developers have previously beendescribed in a number of patents and technical articles. Spenceand'Carroll U. S. Patent 2,640,776, issued June 2, 1953, enumerates anumber of couplersuseful in color developers which have been foundparticularly useful in my invention. Typical of such coupers forproducing cyan images are:

COUPLER (l4) 5 (p amylphenoxybenzenesulfonamino) 1 naphthol (15)2,4-dichloro-S-palmitylammo-l-naphthol (l6) S-hydroxyl-a-naphthoyl- 1,2,3,4 tetrahydroquinoline ( l7) 5 -phenoxyacetaminol-naphthol 18)2-acetylamino-5-methylphenol (19) 2-{4'- a-(4"-tert.amylphenoxyl-n-butyrylammo] benzoylamino}-4-chloro-5-methylphenol (20)2,4-dichloro-5- (p-toluenesulfamlno) -l-naphtbol Negative devel0pment.Aportion of a gelatino-silverbromiodide emulsion which-had beensensitized with a sulfur compound and a gold compound as mentioned abovewas coated on a cellulose acetate support (identified as coating 1below). The oleyl ether of a polyethylene glycol having a molecularweight greater than 300 was added to a second portion of this emulsionat a concentration of 5 grams'of the oleyl ether per mole of silverhalide, and the emulsion was coated on a cellulose acetate support(identified as coating 2 below). One strip of each coating was exposedfor second to a SOD-watt, 3000 K. light source on an Eastman type lbsensitometer. The exposed coatings were then developed for three minutesin developer A having the following composition:

Sodium hexametaphosphate ..g 0.5. Sodium sulfite (anhydrous) g 40.0N-rnethyl-p-aminophenolsulfate g 5.0 Hydroquinone g 2.0. r Sodiumcarbonate (monohydrate) g- 25.0 Potassium bromide g 1.0 Potassium iodide(0.1% solution) cc 2 Water to makeone liter. (pH was 10.1 at 70 F.)

1 An exposed strip of each coating was developed in a.

chlorophenyl)thiazolidine was added. This second dew veloper isidentified below as developer B. The series-of coatings was then fixedin a solution having the following composition: a g

Sodium thiosulfate (pentahydrate) -g 200 Sodium sulfite (anhydrous) g 10Water to make one liter.

The coatings were washed in the usual manner and dried.

Color development-Two additional strips of each of the above coatings (1and 2) were exposed and processed in developers A and B described aboveand washed for two minutes. These coatings were then given a reversalexposure for ten seconds (flash) with No. 2 Photofloods set at 52 inchdistance. The coatings were then developed for five minutes in adeveloper having the following 1 4-amino-3-methyl-N,N -diethylanilinehydrochloride. 5 2,4-dich1oro-5- (p-toluenesulfonamido) -1naphthol.

The coatings were washed for ten minutes and treated for two minutes ina silver bleach bath having the following composition:

Potassium ferricyanide g a 100 Potassium. bromide g Borax g 7.5 Boricacid g 5.0

Water to make one liter.

The coatings were then treated for two minutes in a fixing bath havingthe composition given above, washed and dried. The speed and fog foreach of the above coatings were measured after the washing followingnegative development, while the D-max. on the color developed strips wasmeasured after completion of the process (i. e., after cyandevelopment). The speed figures given below were determined according tothe formula: speed equals 100' (1-log E) wherein E is the exposure inmeter candle seconds required to give a density of 0.3 above fog. Theresults obtained were as follows:

NEGATIVE DEVELOPMENT Coating Developer Speed Fog COLOR DEVELOPMENTCoating Developer D-Max.

A 2.36 B 4.00 A 3.27 B 4.00

6 Example 2 An' ordinary photographic gelatino-silver-bromiodide:

emulsion was divided into two portions and 5 g. of the oleyl ether ofpolyethylene glycol per mole of silver halide was added to one. portion,and these portions coated on separatecellulose acetate supports,identified (1) (unsensitized) and (2) (sensitized). The coatings wereexposed and processed exactly as described in Example 1 above exceptthat 4-carboxy-2-(m-nitrophenyl)thiazolidine was added to one of theblack-and-white developers in the amount of 0.03 g. per liter ofdeveloper in place of the corresponding chloro compound employed inExample 1. The .developer containing no thiazolidine com-- pound isidentified as A below, while the developer containing said compound isidentified as B below. The

processed coatings were then'examined, as in the caseof Example 1, forfog and speed after the first develop-' ment and the color density(D-max.) after the color development. The results obtained were asfollows:

NEGATIVE DEVELOPMENT Coating Developer Speed Fog A 0. 39 B 119 0.12 A121 0.58 B 126 0.16

COLOR DEVELOPMENT Coating Developer D-Max.

A 2.36 B 4. 00 A 3.27 B 4.00-

cation' Serial No. 550,495, filed December 1, 1955, in

the name of D. E. Piper.

The color-forming developers useful in my invention have been previouslydescribed in the prior art, and my in vention is not to be restricted tothe use of any particular color-forming developer. The most useful ofsuch colorforming developers are the phenylenediamines and substitutedderivatives thereof. Typical of such color-forming developers are thesulfonamido substituted p-phenylenediamines disclosed in Weissberger eta1. U. S. Patent 2,548,574, issued April 10, 1951, the substitutedp-phenylenediamines disclosed in Weissberger et al. U. S. Patents2,552,240-2, issued May 8, 1951, and the substituted pphenylenediaminesdisclosed in Weissberger et al. U. S. Patent 2,566,271, issued August28, 1951. Other phenylenediamine color-forming developers can beemployed to like advantage in the process of my invention.

While the above examples primarily illustrate the use of photographicemulsions which have been chemically sensitized with the oleyl ether ofpolyethylene glycol, it is to be understood that other condensates ofalkylene oxides can be advantageously employed to sensitize suchemulsions. Such condensates are generally referred to as alkylene oxidepolymers, the alkylene oxides generally containing from 2 to 4 carbonatoms. Such alkylene oxide polymers'include polyalkylene glycols andconden sation products of alkylene oxides with organic compounds 7containing an active hydrogen. atom, such as alcohols, amines,mercaptans, acids, amides, etc. Generally, such alkylene oxide. polymershave a molecular weight of at. least 300,. asfsliown in U.S.-application Serial No. 50,495 mentioned above. It is to be furtherunderstoodlilattheemulsions. employedin my invention need notbechemically sensitized, although particularly usefulresults have beenobtainedwith emulsions which havebeenchemically' sensitized with suchalkylene oxide polymers.

What I claim as my invention and. desire secured by Letters Patent ofthe UnitedStates is:

1. A photographic developer having. a reduced tendency to fogphotographic silver halide emulsions comprising an alkaline solution of(1).a silver halide developing agent selected from the group consistingof .polyhydroxybenzenes, N-monoalk-ylaminophenols, and mixtures of saidpolyhydroxybenzenes and N-monoallgylaminophenols and at least mg. perliter of solution of (2) a compound selected from. the group consistingof (18) those represented by the following general formula:

wherein R represents a member selected from the group consisting of ahydrogen atom, a lower alkyl group containing from 1 to 2 carbon atomsand a monocyclic aryl group of the benzene series, and (B) awater-soluble salt of said compound.

2. A photographic developer having a reduced tendency to fogphotographic silver halide emulsions comprising an alkaline solution ofhydroquinone and N-methyl-p-aminophenol, and at least 10 mg. per literof solution of a watersoluble salt of a compound selected from thoserepre: sented by the following general formula:

wherein' R represents a monocyclic aryl group of the benzene series.

'4. A- photographic developer having a reduced tendency to fogphotographic silver=halide emulsions comprising an alkalinesolution of(1) a photographiesilver halide developer selected from the groupconsisting of hydroquinone,N-methyl-p-aminophenoland;mixtures-ofhydroquinone (2) anN-methyl-p-aminophenol,an alkalimetal sulfite and (3) at least 10 mg.per liter ofsolution of a water-soluble salt of a compound selected fromthose represented-by the following general formula:

wherein R represents a monocyclic =aryl .groupsof" the benzene .series.

5. A-photographic developer having a reduced tendency:

to fog photographic silver halide emulsions comprising an alkalineaqueous solution of hydroquinone, N-methyl-paminophenol and at least-1'0mg. per liter of solution, of a water soluble salt of4-carboxy-2-(p-chlorophenyl)- thiazolidine.

6. A photographic developer having a reduced tendency to fogphotographic silver halide emulsions comprising an alkaline aqueoussolution of hydroquinone, N-methyl-paminophehol and at least 10 mg. perliter of solution of a water soluble salt of 4-carboxy-2-(m-nitrophenyl)thiazolidine.

7. In a complete photographic reversal color process wherein amultilayer photographic element containing a plurality .ofdifferentially sensitized photographic silver halide emulsion layers isgiven a first exposure, followed by development in a photographicdeveloper for producing a black-andwhitenegative image and asecond egoposure followed by at least one additional development in a photographicdeveloper for producing a colored image, said colored image bearing acomplementary relationshipto the region of the spectrum to which thephotographic silver halide emulsion has been difierentially sensitized,the step of developing said photographic silver halide emulsion layersafter the first exposure with a black-and-white developer comprising analkaline solution of a silver halide developing agent selected from thegroup consisting of polyhydroxybenzenes, N-monoalkylaminophenols andmixtures of polyhydroxybenzenes and N-monoalk ylaaminophenols andatleast 10 n g per liter of solution of aicompound selectedifrom thegroupconsisting of (1) those represented by the following generalformula:

wherein R represents a member selected from the group consisting of ahydrogen atom, a lower alkyl group containing from 1 to 2 carbon atomsand a monocyclic aryl group of the benzene series, and (2) awater-soluble salt of said compound.

8. In a complete photographic reversal color process wherein amultilayer photographic element containing a plurality of difierentiallysensitized photographic silver halide emulsion layers is given a firstexposure, followed by development in a photographic developer forproducing a black-and-white negative image and a second exposurefollowed by at leastone additional development in a photographicdeveloper for producing a colored image, said colored image bearing acomplementary relationship to the region of the spectrum to which thephotographic silver halide emulsion has been differentially sensitized,the step of developing said first exposed silver halide emulsion layersin a black-and-white photographic developer having a reduced tendency tofog said photographic silver halide emulsions comprising an alkalinesolution of hydroquinone and N-methyl-p-aminophenol, and at least 10 mg.per liter of solution of a watersoluble salt of a compound selected fromthose represented by the following general formula:

wherein R represents a member'selected from the group consistingof ahydrogen atom, a lower alkyl group containing from 1 to 2 carbon atomsand a monocyclic aryl group of the benzene series.

9. In a complete photographic reversal color process wherein amultilayer photographic element containing a plurality of differentiallysensitized photographic silver halide emulsion layers is given a firstexposure, followed by development in a photographic developer forproducing a black-and-white negative image and a second exposurefollowed by at least one additional development in a photographicdeveloper for producing a colored image, said colored image bearing acomplementary relationship to the region of the spectrum to which thephotographic silver halide emulsion has been difierentially sensitized,the step of developing said first exposed silver halide emulsion layersin a black-and-white developer having a reduced tendency to fog saidsilver halide emulsions comprising an alkaline solution of aphotographic silver halide developer selected from the group consistingof hydroquinone, N-methyl-p-aminophenol and mixtures of hydroquinone andN-methyl-p-aminophenol, an alkali metal sulfite and at least mg. perliter of solution of a water-soluble salt of a compound selected fromthose represented by the following general formula:

R-C H2 wherein R represents a monocyclic aryl group of the benzeneseries.

10. In a complete photographic reversal color process wherein amultilayer photographic element containing a plurality of differentiallysensitized photographic silver halide emulsion layers is given a firstexposure, followed by development in a photographic developer forproducing a black-and-white negative image and a second exposurefollowed by at least one additional development in a photographicdeveloper for producing a colored image, said colored image bearing acomplementary relationship to the region of the spectrum to which thephotographic silver halide emulsion has been differentially sensitized,the step of developing said first exposed silver halide emulsion layersin a black-and-white photographic developer having a reduced tendency tofog said photographic silver halide emulsions comprising an aqueoussolution of (1) a photographic silver halide developer selected from thegroup consisting of hydroquinone, N- methyl-p-aminophenol, and mixturesof hydroquinone and N-methyl-p-aminophenol, (2) sodium carbonate, (3) analkali metal sulfite, and (4) a compound selected from those representedby the following general formula:

wherein R represents a monocyclic aryl group of the benzene series.

11. In a complete photographic reversal color process wherein amultilayer photographic element containing a plurality of differentiallysensitized photographic silver halide emulsion layers, at least one ofwhich is chemically sensitized with an alkylene oxide polymer having amo lecular weight of at least 300, said alkylene oxide containing from 2to 4 carbon atoms, is given a first exposure, followed by development ina photographic developer for producing a black-and-white negative imageand at least one additional exposure followed by at least one additionaldevelopment in a photographic developer for producing a colored image,said colored image having a complementary relationship to the region ofthe spectrum to which the photographic silverhalide emulsion has beendifferentially sensitized, the step of developing said first exposedsilver halide emulsion layer in a black-and-white photographic developerhaving a reduced tendency to fog said photographic silver halideemulsions, comprising an alkaline solution of a silver halide developingagent selected from the group consisting of polyhydroxybenzenes, N-monoalkylaminophenols and mixtures of polyhydroxybenzenes andN-monoalkylaminophenols and at least 10 mg. per liter of solution of awater-soluble salt of a compound selected from those represented by thefollowing general formula:

wherein R represents a member selected from the group consisting of ahydrogen atom, a lower alkyl group containing from 1 to 2 carbon atomsand a monocyclic aryl group of the benzene series.

References Cited in the file of this patent UNITED STATES PATENTS2,099,374 Schwarz Nov. 16, 1937 OTHER REFERENCES Chem. Abstracts, 44,1490a (1950).

Chem. Abstracts, 46, 29370 (1952).

Chem. Abstracts, 46, 10025a (1952). Chem. Abstracts, 47, 1514g (1953).Chem. Abstracts, 47, 6803c (1953). Chem. Abstracts, 48, 11394b (1954).Chem. Abstracts, 49, 15575h (1955).

1. A PHOTOGRAPHIC DEVELOPER HAVING A REDUCED TENDENCY TO FOGPHOTOGRAPHIC SILVER HALIDE EMULSIONS COMPRISING AN ALKALINE SOLUTION OF(1) A SILVER HALIDE DEVELOPING AGENT SELECTED FROM THE GROUP CONSISTINGOF POLYHYDROXYBENZENES, N-MONOALKYLAMINORPHENOLS, AND MIXTURES OF SAIDPOLYHYDROXYBENZENES AND N-MONOALKYLAMINOPHENOLS AND AT LEAST 10 MG. PERLITER OF SOLUTION OF (2) A COMPOUND SELECTED FROM THE GROUP CONSISTINGOF (A) THOSE REPRESENTED BY THE FOLLOWING GENERAL FORMULA: